OLS Model

## 
## Call:
## lm(formula = equation, data = fl_pov)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.211930 -0.063175 -0.007283  0.051057  0.276869 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)   
## (Intercept)     -1.185293   0.622157  -1.905  0.06241 . 
## rural            0.153878   0.258799   0.595  0.55475   
## urban            0.083299   0.051566   1.615  0.11240   
## lnmanufacturing  0.092756   0.034704   2.673  0.01008 * 
## lnag             0.040325   0.023152   1.742  0.08758 . 
## lnretail         0.276450   0.080755   3.423  0.00123 **
## lnhealthss       0.363312   0.105548   3.442  0.00116 **
## lnconstruction   0.077380   0.067385   1.148  0.25620   
## lnlesshs         0.173800   0.081454   2.134  0.03770 * 
## lnsinglemom     -0.057206   0.076525  -0.748  0.45817   
## lnblack          0.007684   0.035991   0.213  0.83179   
## lnhispanic       0.047137   0.040613   1.161  0.25119   
## lnuninsured      0.092831   0.187230   0.496  0.62216   
## lnincome_ratio  -0.150950   0.150096  -1.006  0.31931   
## lnteenbirth      0.032004   0.039240   0.816  0.41852   
## lnunmarried      0.093013   0.061724   1.507  0.13800   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1125 on 51 degrees of freedom
## Multiple R-squared:  0.6659, Adjusted R-squared:  0.5676 
## F-statistic: 6.776 on 15 and 51 DF,  p-value: 0.0000001045

The OLS model includes several significant predictor variables including lnhealthss,lnretail,lnmanufacturing, lnlesshs

Visreg OLS Plots

Moran’s Correlation Test for Spatial Dependency

lm.morantest(ols, cont.neighb)
## 
##  Global Moran I for regression residuals
## 
## data:  
## model: lm(formula = equation, data = fl_pov)
## weights: cont.neighb
## 
## Moran I statistic standard deviate = 2.3231, p-value = 0.01009
## alternative hypothesis: greater
## sample estimates:
## Observed Moran I      Expectation         Variance 
##      0.134745905     -0.046940024      0.006116573

P-value=.01009. Spatial dependency detected in the dataset, reject null hypothesis (no spatial correlation in residuals)

LaGrange Multiplier Test

lm.LMtests(ols, cont.neighb, test="all")
## 
##  Lagrange multiplier diagnostics for spatial dependence
## 
## data:  
## model: lm(formula = equation, data = fl_pov)
## weights: cont.neighb
## 
## LMerr = 2.5538, df = 1, p-value = 0.11
## 
## 
##  Lagrange multiplier diagnostics for spatial dependence
## 
## data:  
## model: lm(formula = equation, data = fl_pov)
## weights: cont.neighb
## 
## LMlag = 2.5152, df = 1, p-value = 0.1128
## 
## 
##  Lagrange multiplier diagnostics for spatial dependence
## 
## data:  
## model: lm(formula = equation, data = fl_pov)
## weights: cont.neighb
## 
## RLMerr = 0.25252, df = 1, p-value = 0.6153
## 
## 
##  Lagrange multiplier diagnostics for spatial dependence
## 
## data:  
## model: lm(formula = equation, data = fl_pov)
## weights: cont.neighb
## 
## RLMlag = 0.21392, df = 1, p-value = 0.6437
## 
## 
##  Lagrange multiplier diagnostics for spatial dependence
## 
## data:  
## model: lm(formula = equation, data = fl_pov)
## weights: cont.neighb
## 
## SARMA = 2.7677, df = 2, p-value = 0.2506

LMerr=0.1100


LMlag=0.1128


RLMerr=0.6153


RLMlag=0.6437


SARMA= 0.2506


Spatial error or spatial lag model would be best.

Spatially Lagged X Model

SLX.model <- spatialreg::lmSLX(equation, data=fl_pov, cont.neighb)
summary(SLX.model)
## 
## Call:
## lm(formula = formula(paste("y ~ ", paste(colnames(x)[-1], collapse = "+"))), 
##     data = as.data.frame(x), weights = weights)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.161625 -0.042118 -0.000216  0.048149  0.182283 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         -3.80184    2.00676  -1.895 0.066212 .  
## rural                0.22298    0.29174   0.764 0.449662    
## urban                0.11494    0.05771   1.992 0.054016 .  
## lnmanufacturing      0.12268    0.03812   3.218 0.002728 ** 
## lnag                 0.05156    0.02218   2.325 0.025821 *  
## lnretail             0.30018    0.07594   3.953 0.000346 ***
## lnhealthss           0.33824    0.11627   2.909 0.006176 ** 
## lnconstruction       0.03111    0.07117   0.437 0.664591    
## lnlesshs             0.24696    0.07955   3.105 0.003702 ** 
## lnsinglemom         -0.05593    0.08605  -0.650 0.519797    
## lnblack              0.04431    0.03775   1.174 0.248207    
## lnhispanic          -0.01840    0.05123  -0.359 0.721581    
## lnuninsured          0.07605    0.20763   0.366 0.716302    
## lnincome_ratio       0.02867    0.15803   0.181 0.857044    
## lnteenbirth          0.06476    0.04093   1.582 0.122372    
## lnunmarried          0.13189    0.06962   1.894 0.066228 .  
## lag.rural            1.15152    0.51489   2.236 0.031611 *  
## lag.urban            0.33223    0.12356   2.689 0.010796 *  
## lag.lnmanufacturing  0.10188    0.09464   1.076 0.288874    
## lag.lnag             0.09856    0.04809   2.049 0.047756 *  
## lag.lnretail         0.22230    0.20212   1.100 0.278705    
## lag.lnhealthss      -0.36290    0.26199  -1.385 0.174527    
## lag.lnconstruction  -0.00185    0.19276  -0.010 0.992397    
## lag.lnlesshs        -0.43914    0.19831  -2.214 0.033223 *  
## lag.lnsinglemom      0.12321    0.20901   0.589 0.559216    
## lag.lnblack         -0.04880    0.09097  -0.536 0.594918    
## lag.lnhispanic      -0.07987    0.10571  -0.756 0.454846    
## lag.lnuninsured      0.30868    0.51728   0.597 0.554413    
## lag.lnincome_ratio   0.42511    0.36337   1.170 0.249724    
## lag.lnteenbirth      0.08151    0.09217   0.884 0.382376    
## lag.lnunmarried      0.39688    0.11878   3.341 0.001953 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.09507 on 36 degrees of freedom
## Multiple R-squared:  0.8316, Adjusted R-squared:  0.6912 
## F-statistic: 5.924 on 30 and 36 DF,  p-value: 0.0000004974


It looks like some of the lag variables are significant


summary(spatialreg::impacts(SLX.model, cont.neighb), zstats = TRUE)[["pzmat"]]
##                       Direct     Indirect        Total
## rural           0.4446806472 0.0253236263 0.0200477943
## urban           0.0463883266 0.0071718323 0.0029606849
## lnmanufacturing 0.0012890520 0.2817126630 0.0261975419
## lnag            0.0200684510 0.0404154964 0.0027134722
## lnretail        0.0000772833 0.2714045632 0.0211018050
## lnhealthss      0.0036239322 0.1660029939 0.9215749866
## lnconstruction  0.6619797355 0.9923437214 0.8964755149
## lnlesshs        0.0019056880 0.0268041254 0.3742232689
## lnsinglemom     0.5156703661 0.5555340302 0.7741950207
## lnblack         0.2405003865 0.5916181336 0.9662263740
## lnhispanic      0.7194834523 0.4499312276 0.3563418815
## lnuninsured     0.7141585725 0.5506780765 0.4869107567
## lnincome_ratio  0.8560258964 0.2420366067 0.2790049845
## lnteenbirth     0.1136252026 0.3765077581 0.1899708337
## lnunmarried     0.0581722443 0.0008340691 0.0002792914

Significant variables in analysis include rural, urban, lnmanufacturing, lnag, lnretail, lnunmarried

Spatial Lag Model

sp.lag.model <- spatialreg::lagsarlm(equation, data=fl_pov, cont.neighb)
summary(sp.lag.model, Nagelkerke = TRUE)
## 
## Call:
## spatialreg::lagsarlm(formula = equation, data = fl_pov, listw = cont.neighb)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.1941231 -0.0638849 -0.0074391  0.0404584  0.2835548 
## 
## Type: lag 
## Coefficients: (asymptotic standard errors) 
##                  Estimate Std. Error z value  Pr(>|z|)
## (Intercept)     -1.543273   0.555321 -2.7791 0.0054516
## rural            0.077834   0.219494  0.3546 0.7228847
## urban            0.088421   0.044629  1.9812 0.0475643
## lnmanufacturing  0.091538   0.029419  3.1116 0.0018610
## lnag             0.037578   0.019633  1.9140 0.0556178
## lnretail         0.255516   0.068874  3.7099 0.0002073
## lnhealthss       0.318512   0.092958  3.4264 0.0006116
## lnconstruction   0.083052   0.057243  1.4509 0.1468185
## lnlesshs         0.192075   0.069031  2.7825 0.0053948
## lnsinglemom     -0.034916   0.066575 -0.5245 0.5999596
## lnblack          0.014295   0.030597  0.4672 0.6403558
## lnhispanic       0.033636   0.035046  0.9598 0.3371774
## lnuninsured      0.069739   0.159868  0.4362 0.6626694
## lnincome_ratio  -0.114425   0.128014 -0.8938 0.3714042
## lnteenbirth      0.037512   0.033414  1.1226 0.2615867
## lnunmarried      0.074536   0.052358  1.4236 0.1545655
## 
## Rho: 0.25587, LR test value: 2.8514, p-value: 0.091292
## Asymptotic standard error: 0.13205
##     z-value: 1.9376, p-value: 0.052667
## Wald statistic: 3.7545, p-value: 0.052667
## 
## Log likelihood: 61.87941 for lag model
## ML residual variance (sigma squared): 0.0090882, (sigma: 0.095332)
## Nagelkerke pseudo-R-squared: 0.6798 
## Number of observations: 67 
## Number of parameters estimated: 18 
## AIC: -87.759, (AIC for lm: -86.907)
## LM test for residual autocorrelation
## test value: 1.525, p-value: 0.21687


P=.091292, model is not significant. Spatial lag model not appropriate?


summary(spatialreg::impacts(sp.lag.model, listw = cont.neighb, R=100), zstats = TRUE)[["pzmat"]]
##                       Direct  Indirect       Total
## rural           0.8588070657 0.8940939 0.863766360
## urban           0.0399045027 0.3257214 0.082537864
## lnmanufacturing 0.0029798597 0.2454009 0.012479823
## lnag            0.0500012937 0.3063356 0.082356281
## lnretail        0.0001572530 0.2365658 0.004436958
## lnhealthss      0.0003779642 0.1924958 0.001280392
## lnconstruction  0.1549220266 0.4010599 0.185042744
## lnlesshs        0.0029231991 0.2511549 0.012441264
## lnsinglemom     0.6476491850 0.8350248 0.687078732
## lnblack         0.6577398070 0.7037136 0.655939111
## lnhispanic      0.3689980179 0.6111192 0.402821009
## lnuninsured     0.6402059504 0.7533017 0.659254597
## lnincome_ratio  0.4110766736 0.5957018 0.438155159
## lnteenbirth     0.2146335575 0.4204202 0.250003750
## lnunmarried     0.2365760206 0.4067398 0.249166926


P=.009. Significant variables include lnretail, lnhealthss, lnlesshs


Spatial Error Model

sp.err.model <- spatialreg::errorsarlm(equation, data=fl_pov, cont.neighb)
summary(sp.err.model, Nagelkerke = TRUE)
## 
## Call:
## spatialreg::errorsarlm(formula = equation, data = fl_pov, listw = cont.neighb)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.191807 -0.059441 -0.010568  0.055655  0.255013 
## 
## Type: error 
## Coefficients: (asymptotic standard errors) 
##                  Estimate Std. Error z value   Pr(>|z|)
## (Intercept)     -1.348885   0.533437 -2.5287  0.0114497
## rural           -0.125390   0.208385 -0.6017  0.5473568
## urban            0.031479   0.039545  0.7960  0.4260154
## lnmanufacturing  0.090685   0.029166  3.1093  0.0018756
## lnag             0.022970   0.019106  1.2022  0.2292711
## lnretail         0.236081   0.061315  3.8503  0.0001180
## lnhealthss       0.386307   0.093113  4.1488 0.00003342
## lnconstruction   0.068321   0.051746  1.3203  0.1867314
## lnlesshs         0.233575   0.062175  3.7568  0.0001721
## lnsinglemom     -0.088644   0.062287 -1.4232  0.1546910
## lnblack          0.026299   0.027717  0.9488  0.3427101
## lnhispanic       0.033171   0.037976  0.8735  0.3824008
## lnuninsured      0.199352   0.158989  1.2539  0.2098875
## lnincome_ratio  -0.083870   0.116910 -0.7174  0.4731339
## lnteenbirth      0.026508   0.029111  0.9106  0.3625120
## lnunmarried      0.024901   0.048140  0.5173  0.6049679
## 
## Lambda: 0.5859, LR test value: 6.7214, p-value: 0.0095261
## Asymptotic standard error: 0.11244
##     z-value: 5.2108, p-value: 0.00000018803
## Wald statistic: 27.152, p-value: 0.00000018803
## 
## Log likelihood: 63.8144 for error model
## ML residual variance (sigma squared): 0.0079102, (sigma: 0.088939)
## Nagelkerke pseudo-R-squared: 0.69777 
## Number of observations: 67 
## Number of parameters estimated: 18 
## AIC: NA (not available for weighted model), (AIC for lm: -86.907)

Significant variables include lnlesshs, lnretail, lnhealthss, lnmanufacturing

Comparing Contiguity Models

SLX R^2=0.6912
SLX P=0.0000004974

Lag R^2=0.6798
Lag P=0.21687

Err R^2=0.698
Err P=.0095261

Appears that the spatially lagged X model is the best fit

Spatial Hausman Test of Error Model

This test will see if the results of the analysis verify the use of the selected model

spatialreg::Hausman.test(sp.err.model)
## 
##  Spatial Hausman test (asymptotic)
## 
## data:  NULL
## Hausman test = 21.899, df = 16, p-value = 0.1465

Based on the p value of 0.1465, we fail to reject null hypothesis that the estimation method should yield coefficients appropriate for a spatial error model. Spatial error model is appropriate.


Sadie Break



Nested Spatial Durbin Models

summary(sd.err, Nagelkerke = TRUE)
## 
## Call:
## spatialreg::errorsarlm(formula = equation, data = fl_pov, listw = cont.neighb, 
##     etype = "emixed")
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.1601513 -0.0416545  0.0016086  0.0440903  0.1699257 
## 
## Type: error 
## Coefficients: (asymptotic standard errors) 
##                        Estimate  Std. Error z value       Pr(>|z|)
## (Intercept)         -3.48856169  1.48990406 -2.3415      0.0192081
## rural                0.11374914  0.19992266  0.5690      0.5693794
## urban                0.10892082  0.04217002  2.5829      0.0097975
## lnmanufacturing      0.12445530  0.02656529  4.6849 0.000002801185
## lnag                 0.05692023  0.01528024  3.7251      0.0001952
## lnretail             0.33729957  0.05833540  5.7821 0.000000007379
## lnhealthss           0.35115281  0.07791564  4.5068 0.000006580234
## lnconstruction       0.03440683  0.05357488  0.6422      0.5207307
## lnlesshs             0.26539296  0.05983681  4.4353 0.000009195313
## lnsinglemom         -0.07282453  0.06012351 -1.2112      0.2258000
## lnblack              0.04508305  0.02832751  1.5915      0.1114986
## lnhispanic           0.00086885  0.03360570  0.0259      0.9793735
## lnuninsured          0.03011682  0.14446658  0.2085      0.8348627
## lnincome_ratio       0.01791462  0.12211179  0.1467      0.8833635
## lnteenbirth          0.09143313  0.03111775  2.9383      0.0033002
## lnunmarried          0.10181182  0.04825709  2.1098      0.0348773
## lag.rural            1.04342564  0.38952971  2.6787      0.0073913
## lag.urban            0.33130202  0.09243425  3.5842      0.0003381
## lag.lnmanufacturing  0.08290062  0.06691287  1.2389      0.2153700
## lag.lnag             0.09488781  0.03732963  2.5419      0.0110255
## lag.lnretail         0.38790429  0.16016778  2.4219      0.0154412
## lag.lnhealthss      -0.42582441  0.20168555 -2.1113      0.0347441
## lag.lnconstruction   0.01176520  0.14300478  0.0823      0.9344309
## lag.lnlesshs        -0.34967744  0.15634211 -2.2366      0.0253114
## lag.lnsinglemom      0.12308154  0.17166633  0.7170      0.4733857
## lag.lnblack         -0.06863803  0.07583983 -0.9050      0.3654446
## lag.lnhispanic      -0.07482881  0.07463451 -1.0026      0.3160523
## lag.lnuninsured      0.03457217  0.36834813  0.0939      0.9252225
## lag.lnincome_ratio   0.41933819  0.29776982  1.4083      0.1590532
## lag.lnteenbirth      0.16284989  0.07724589  2.1082      0.0350136
## lag.lnunmarried      0.33491711  0.09556195  3.5047      0.0004571
## 
## Lambda: 0.57034, LR test value: 5.3879, p-value: 0.020277
## Asymptotic standard error: 0.11513
##     z-value: 4.9541, p-value: 0.00000072684
## Wald statistic: 24.543, p-value: 0.00000072684
## 
## Log likelihood: 86.0926 for error model
## ML residual variance (sigma squared): 0.0040924, (sigma: 0.063972)
## Nagelkerke pseudo-R-squared: 0.84457 
## Number of observations: 67 
## Number of parameters estimated: 33 
## AIC: NA (not available for weighted model), (AIC for lm: -102.8)


R^2=0.84457, P=0,020277, error model looks appropriate

Impacts Matrix Analysis

summary(spatialreg::impacts(sd.err, listw = cont.neighb, R = 100), zstats = TRUE)[["pzmat"]]
##                            Direct     Indirect        Total
## rural           0.569379410515021 0.0073912880 0.0191745521
## urban           0.009797452433238 0.0003381243 0.0002951369
## lnmanufacturing 0.000002801185230 0.2153699987 0.0087373887
## lnag            0.000195248381183 0.0110254894 0.0005331110
## lnretail        0.000000007378536 0.0154412036 0.0002367899
## lnhealthss      0.000006580234089 0.0347440970 0.7371823694
## lnconstruction  0.520730701109836 0.9344308963 0.7969056580
## lnlesshs        0.000009195313378 0.0253113758 0.6538144498
## lnsinglemom     0.225800046803441 0.4733856587 0.8063359597
## lnblack         0.111498594865494 0.3654445564 0.8042019913
## lnhispanic      0.979373499399558 0.3160523131 0.3771322255
## lnuninsured     0.834862695500020 0.9252225047 0.8816482836
## lnincome_ratio  0.883363530964298 0.1590532401 0.2462620890
## lnteenbirth     0.003300226077460 0.0350135726 0.0104169963
## lnunmarried     0.034877348778877 0.0004571019 0.0004917500


Significant impacts include lnretail, lnmanufacturing, urban, retail, lnag, lnunmarried,lnteenbirth. Spatial Durbin Error Model may be most appropriate?


LR.Sarlm(sd.err,sp.err.model)
## 
##  Likelihood ratio for spatial linear models
## 
## data:  
## Likelihood ratio = 44.556, df = 15, p-value = 0.00008994
## sample estimates:
##       Log likelihood of sd.err Log likelihood of sp.err.model 
##                        86.0926                        63.8144


P=.00008994, reject null, do not restrict model, Spatial error durbin model is appropriate.


K-Nearest Neighbor Analysis: Distance Lag Model

summary(all.dist.lag.k1, Nagelkerke = TRUE)
## 
## Call:
## spatialreg::lagsarlm(formula = equation, data = fl_pov, listw = all.dist.neighb.k1)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.2120059 -0.0617265 -0.0079057  0.0386980  0.2862156 
## 
## Type: lag 
## Coefficients: (asymptotic standard errors) 
##                  Estimate Std. Error z value  Pr(>|z|)
## (Intercept)     -1.437645   0.566918 -2.5359 0.0112159
## rural            0.107417   0.222051  0.4837 0.6285658
## urban            0.085909   0.045046  1.9071 0.0565062
## lnmanufacturing  0.093187   0.029804  3.1267 0.0017679
## lnag             0.035180   0.019885  1.7692 0.0768628
## lnretail         0.277058   0.069326  3.9965 0.0000643
## lnhealthss       0.336913   0.093310  3.6107 0.0003054
## lnconstruction   0.078225   0.057859  1.3520 0.1763788
## lnlesshs         0.193254   0.070116  2.7562 0.0058481
## lnsinglemom     -0.047369   0.066330 -0.7141 0.4751433
## lnblack          0.014666   0.031047  0.4724 0.6366472
## lnhispanic       0.040376   0.035075  1.1511 0.2496752
## lnuninsured      0.067136   0.162385  0.4134 0.6792842
## lnincome_ratio  -0.116513   0.130013 -0.8962 0.3701637
## lnteenbirth      0.038407   0.034011  1.1293 0.2587799
## lnunmarried      0.080346   0.052957  1.5172 0.1292180
## 
## Rho: 0.15037, LR test value: 1.7448, p-value: 0.18653
## Asymptotic standard error: 0.11649
##     z-value: 1.2909, p-value: 0.19675
## Wald statistic: 1.6663, p-value: 0.19675
## 
## Log likelihood: 61.32609 for lag model
## ML residual variance (sigma squared): 0.0093165, (sigma: 0.096522)
## Nagelkerke pseudo-R-squared: 0.67447 
## Number of observations: 67 
## Number of parameters estimated: 18 
## AIC: -86.652, (AIC for lm: -86.907)
## LM test for residual autocorrelation
## test value: 0.049768, p-value: 0.82347

K-Nearest Neighbor Analysis: Distance Error Model

summary(all.dist.err.k1, Nagelkerke = TRUE)
## 
## Call:
## spatialreg::errorsarlm(formula = equation, data = fl_pov, listw = all.dist.neighb.k1)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.2269206 -0.0587658 -0.0047593  0.0470413  0.2687581 
## 
## Type: error 
## Coefficients: (asymptotic standard errors) 
##                  Estimate Std. Error z value   Pr(>|z|)
## (Intercept)     -1.252963   0.531852 -2.3558  0.0184804
## rural           -0.133576   0.218750 -0.6106  0.5414430
## urban            0.040883   0.042232  0.9681  0.3330071
## lnmanufacturing  0.087987   0.029736  2.9590  0.0030867
## lnag             0.019652   0.021507  0.9137  0.3608599
## lnretail         0.274675   0.064526  4.2568 0.00002073
## lnhealthss       0.365105   0.092468  3.9484 0.00007866
## lnconstruction   0.065419   0.054189  1.2072  0.2273429
## lnlesshs         0.234528   0.064005  3.6642  0.0002481
## lnsinglemom     -0.080518   0.063750 -1.2630  0.2065774
## lnblack          0.027206   0.028823  0.9439  0.3452196
## lnhispanic       0.037424   0.037056  1.0099  0.3125329
## lnuninsured      0.138577   0.160576  0.8630  0.3881381
## lnincome_ratio  -0.065958   0.120856 -0.5458  0.5852323
## lnteenbirth      0.032470   0.031173  1.0416  0.2975875
## lnunmarried      0.018863   0.050774  0.3715  0.7102604
## 
## Lambda: 0.39437, LR test value: 3.5368, p-value: 0.060023
## Asymptotic standard error: 0.12098
##     z-value: 3.2596, p-value: 0.0011155
## Wald statistic: 10.625, p-value: 0.0011155
## 
## Log likelihood: 62.22206 for error model
## ML residual variance (sigma squared): 0.0086472, (sigma: 0.09299)
## Nagelkerke pseudo-R-squared: 0.68306 
## Number of observations: 67 
## Number of parameters estimated: 18 
## AIC: NA (not available for weighted model), (AIC for lm: -86.907)

Comparing Models


Distance Lag Model R^2=0.67447 P=0.18653 AIC=-86.652


Distance Error Model R^2=0.68306 P=0.060023 AIC=-88.444


Distance error model is better fit than distance lag model


AIC Values of Best Models

AIC(SLX.model)
## [1] -102.7973
AIC(sd.err)
## [1] -106.1852
AIC(all.dist.err.k1)
## [1] -88.44413


The best model appears to be the spatial durbin error model, with an AIC value of -106.1852. The second best model is the Spatially lagged X model, with an AIC value of -102.7973. The third best model is the distance error model.


Mapping Results


I will use the spatial durbin error model for my map since it had the smallest AIC value of the top three models I tested.


dist.err.data <- summary(sd.err, correlation=TRUE, Nagelkerke = TRUE)

dist.err.output <- cbind.data.frame(fl_pov$FIPS,
                                    dist.err.data$fitted.values, 
                                    dist.err.data$residual, 
                                    fl_pov$child.pov.2016, 
                                    fl_pov$lnsinglemom, 
                                    fl_pov$lnuninsured, 
                                    fl_pov$lnlesshs, 
                                    fl_pov$lnincome_ratio,
                                    fl_pov$lnteenbirth,
                                    fl_pov$lnunemployment,
                                    fl_pov$lnhealthss,
                                    stringsAsFactors = FALSE)

#Renaming columns
colnames(dist.err.output) <- c("fips","fitted","resid","childpov",
                        "single_mom","uninsured","less_hs","income_ratio","Teen_births","Unemployment","lnhealthss")







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